1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Help finding eigenvectors to simple 2x2 matrix

  1. Mar 12, 2010 #1
    1. The problem statement, all variables and given/known data
    Find a fundamental set of real solutions of the system.
    x'=[-0.5 1 ]x
    [-1 -0.5]

    3. The attempt at a solution
    I calculated the eigenvalues to be r1 = -0.5+i and r2 = -0.5-i
    Then, attempting to calculate the eigenvectors,
    I plugged the numbers into the system
    [-0.5+0.5-i 1][v1] = [0]
    [-1 -0.5+0.5-i ][v2] [0]
    which simplifies to be
    [-i 1] [v1] = [0]
    [-1 -i ][v2] [0]
    afer matrix multiplication, I get two formulas
    -1(v1)i+(v2)=0
    -1(v1)-(v2)i=0
    However, I am at a loss for the next step. Usually when I am finding the eigenvector those two equations will have the same ratio. Please advise.
     
  2. jcsd
  3. Mar 12, 2010 #2

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    Your two formulas do have the same ratio:wink:...Just multiply the second equation by [itex]i[/itex].
     
  4. Mar 12, 2010 #3
    thanks guy! I can't believe i didn't see that!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Help finding eigenvectors to simple 2x2 matrix
Loading...